本研究採用分層叢集抽樣，從台北市十二行政區中，按比例抽出36所學校。受試者含1-9年級學生合計5475人，有效樣本4917人達89.8%。自編測驗信度、效度考驗：α係數達.80，效標關連效度在.21到.70之間，與智力測驗之相關在各年級均達.01顯著水準，專家效度良好。研究發現包括二部份：

一、邏輯概念之發展：有關台北市立國民中小學學生邏輯概念發展狀況研究結果如次 (1) 形式運思階段之前，兒童可以解答部份的命題邏輯問題。 (2) 具體內容的ＭＰ規則和常見的遞移性關係的遞移推理，分別在國小一年級、及國小四年級已達到發展高原。 (3) 從具體運思到形式運思階段，並沒有發現階段性跳躍的成長現象，邏輯概念發展大致上是向上發展的型態。 (4) 二元運算系統在8,9年級(14、15歲左右)--也就是皮亞傑所指的形式運思階段達到平衡的時期，只能做大約18%?32%的題目，沒有證據顯示大部份的受試者，已經完成了具有「群與格」特徵的命題邏輯結構。本研究的假設一、假設二均未獲得支持。皮亞傑理論對學生的邏輯概念發展有低估和高估的現象。一方面低估了國小中低年級兒童在簡單邏輯規則的發展，另一方面高估了青少年在困難的邏輯規則上所能達到的成就。

二、邏輯概念與數學之相關性：在邏輯與數學的相關性研究方面獲得以下結論： (1) 邏輯成績與數學成績的相關在各年級學生中，均達.0001顯著水準。大部份年級數學成績與智力的相關，大於數學成績與邏輯概念的相關。 (2) 年級對邏輯概念的影響效果顯著，當控制智力高低及數學成就好壞二個因素之後，邏輯概念隨年級而增進。 (3) 數學成就對邏輯概念的影響效果顯著，對各年級學生而言，高數學成就組學生的邏輯概念比其他二組好。但數學成就中等和低等的二組受試者之間，當智力的百分等級在35?56之間時，邏輯概念沒有差異。 (4) 變異數分析顯示，以年級、數學成就與智力的線性模式，可以解釋邏輯概念所有變異量中的63%。共變異數分析顯示，排除智力的影響之後，年級、數學成就仍是可以解釋邏輯概念所有變異量中的63%，與變異數分析結果一致。

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